Ukrainian Energy Minister Yuri Prodan (r.) walks past Gazprom Chief Executive Alexei Miller after EU-Ukraine-Russia energy negotiations at the EU commission representation in Berlin last week. Gazprom today said it would extend the deadline by a week for Ukraine to pay its gas bill.

Thomas Peter/Reuters

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Moscow — It looks like the Kremlin is breaking out the carrots and sticks in its dealings with Ukraine.

Russia's state gas monopoly Gazprom gave Ukraine another week's grace Monday, extending a deadline that would have shut off gas deliveries if Kiev didn't pony up an estimated $4 billion it is thought to owe for past supplies.

That little hint of reasonableness from Moscow was accompanied by the suggestion that Gazprom might negotiate a lower price if Ukraine pays off its debt. It contrasts sharply with what looks like a ramping-up of unofficial Russian participation in the insurrection in Ukraine's east.

Experts say it's a complex game in which the Kremlin opens a few windows for Ukraine's new president, Petro Poroshenko, to come to Moscow and make a deal while ensuring that Mr. Poroshenko gets no respite from the simmering strife in the east.

"Vladimir Putin understands that he's going to have to reach agreement with Poroshenko at some point. The game right now is to maximize Moscow's leverage before that," says Sergei Strokan, foreign affairs columnist with the pro-business Moscow daily Kommersant.

Gazprom acknowledged receipt of $786 million on Monday from Ukraine's Naftogaz, which Ukrainian leaders claim completely extinguishes their past debt. Russia, which canceled discounts given to former Ukrainian President Viktor Yanukovych after he was overthrown in late February, insists it's less than a quarter of what is owed.

Nevertheless, Gazprom backed off its threat to introduce a "prepayment" scheme today, which would have led to an immediate shutdown of gas supplies, and invited the Ukrainians back to the bargaining table.

Russia insists that Ukraine stick to the terms of a 2009 deal and pay $485 per thousand cubic meters of gas, the highest price in all of Europe. Ukrainian interim Prime Minister Arseniy Yatsenyuk insisted last week that Ukraine was willing to continue paying the $268 that included the discounts given to Mr. Yanukovych in return for his political loyalty to Moscow.

But in announcing Monday's "carrot" of a postponement of the gas deadline for another week, Gazprom also let it be known that it might be willing to renegotiate the future price down to about $385, which is the average amount paid by European countries for Russian gas.

Experts say the gas negotiations may be a dress rehearsal for how Moscow will handle other discussions with Kiev, particularly its demands for constitutional changes that would give more power to Ukraine's restive eastern regions.

"First, pour on the pressure. Force Ukraine to bargain on Moscow's terms. Then, offer a compromise that gives Russia most of what it wanted," says Mr. Strokan.

On the political front, Putin has already debuted a few "carrots" by describing the election that brought Poroshenko to office as "a step forward" and ending provocative Russian military deployments on Ukraine's border.

But amid deepening chaos in eastern Ukraine, a unit of combat-hardened Russian volunteers headed by a former officer of Russia's GRU military intelligence, known as the Vostok Battalion, has moved to take control of the rebellion. Experts say the volunteer brigade, which previously fought in Chechnya and in Russia's 2008 war with Georgia, provides the Kremlin with official deniability while ensuring that Ukraine's inept armed forces are unlikely to prevail any time soon in the conflict.

"The Vostok Battalion, like the threat to switch off the gas, is a 'stick'. This force is ostensibly a non-state actor, but it's basically doing just what the Russian Army would do. When Putin is ready, he can smile at Poroshenko and pull it back," says Strokan. "Let the bargaining begin."